In a popular way to restore an image which has been degraded due to blurring, noise, resolution reduction, or the like, an image is generated utilizing a simulation to apply a degradation process such as blurring to a restored image, and difference between the generated image and the degraded image (i.e., input image) is minimized so as to generate the restored image. However, there are an infinite number of solutions (i.e., pixel values) as candidates for such a restored image, and a unique solution cannot be determined. In order to determine a unique solution, regularization to constrain the solution must be performed. For example, a regularization to reduce a variation in the pixel value between neighboring pixels in the restored image is performed to determine a unique solution.
Patent Document 1 discloses a solution regularization method performed in a manner such that when there is a large difference in the pixel value between neighboring pixels in an input image, the restored image has also a large difference in the pixel value between corresponding neighboring pixels (see, for example, paragraph [0030] of Patent Document 1).
More specifically, first, if there is a large difference in the pixel value between neighboring pixels that form an input image, strength for regularization (called “regularization strength” below) is adaptively assigned to each pixel so as to reduce the regularization strength. Next, the following optimization function E([X]) utilizing the determined regularization strength is determined, and an argument to minimize the value of the above optimization function E([X]) is searched for. Then, a restored image having pixel values given by the argument is generated. In the present application, a vector variable is represented by interposing it between brackets “[ ]” or using a bold font. For example, a variable [X] and a boldfaced variable X in the following formula are the same vector variable:[Formula 1]E(X)=Edata(X)+Ereg(X)  (1)
Here, [X] is a column vector consisting of values of individual pixels, which are arranged in raster scan order. For example, when the number of pixels of the restored image is M, [X]=(Xl, . . . , Xi, . . . , XM)t.
Edata([X]) is called an “error term” and indicates an relationship between an input image and a restored image therefor.
Ereg([X]) is called a “regularization term” and restricts the pixel value computed by the optimization function.
In Patent Document 1, the pixel value computed by the optimization function is restricted to uniformly reduce difference between the pixel values of neighboring pixels values, where the following function is utilized as the regularization term Ereg([X]) (see paragraphs [0067] to [0068] of Patent Document 1).
                    [                  Formula          ⁢                                          ⁢          2                ]                                                                                  E            reg                    ⁡                      (            X            )                          =                              ∑            i                                                          ⁢                                          ⁢                                    g              i                        ·                          (                                                4                  ⁢                                                                          ⁢                                      X                    i                                                  -                                  X                                      i                    +                    1                                                  -                                  X                                      i                    -                    1                                                  -                                  X                                      i                    +                    width                                                  -                                  X                                      i                    -                    width                                                              )                                                          (        2        )            
Here, Xi+1, Xi−1, Xi+width, and Xi−width respectively represent upper, lower, left, and right pixels around the ith pixel. Additionally, gi denotes regularization strength.
When the regularization strength gi is adaptively determined for each pixel, it is possible to perform degradation restoration while maintaining sharpness (i.e., amount of difference between pixel values) of the image of a region where difference in the pixel value between neighboring pixels is large.